"if you say a word over and over, it starts to lose all meaning" Semantic satiation The mouthmand tongue feel like they're doing far more repreparation betwixt the 4 and 3 than between any of the others (understandable, F( eye fvvv )F( ore )->??->Th( r eee )T( ooo ) W (o' n ), with handy ...

His wife is obviously also home twenty minutes early.This means she saved 10 minutes drive both ways to/from the station.So she met him when she had still 10 minutes to go to the station, i.e. at 5:50pm.He was walking from 5 till 5:50, so 50 minutes.

Millisecond-precision timing is very impressive, and this type of thing is also necessary for throwing accurately at long distances. It is something we as humans seem to be almost uniquely good at. Humans are also very good at recognising and following patterns. I reckon that by getting a regular s...

Interesting thoughts. Just a quick quibble: ... and a stellation of a cube is just an octahedron, ... No, the octahedron is the dual of the cube. The cube, does not have any stellations : There are no stellations of the cube, because non-adjacent faces are parallel and thus cannot be extended to mee...

There's a very detailed book "The Tower of Hanoi - Myths and Maths" from 2013 which has a whole chapter devoted to this. The four-peg version is also called Reve's Puzzle, given that name by H.E. Dudeney who was the first to write about this generalization in his 1908 Canterbury Puzzles. T...

Seems like that kind of bias would have to be in the method of flipping rather than the coin itself. Quite so. Here's a demonstration of tossing a coin ten times in a row, getting heads each time. (For full disclosure: that is me, and it took me only about 7 or 8 takes. Sorry, I couldn't resist pos...

What I was thinking is that there are some very large numbers that are useful, or at least used, in various types of mathematical explorations, ponderings or theories, perhaps used in things like cryptography (eg: very large primes) or other esoteric fields, even if its just exploring the nature of...

I plan on painting over the squares of a rubrics cube It's called a Rubik's Cube, named after its inventor Ernö Rubik. Such maze cubes have been designed before. The standard maze cube design was made by Christoph Lohe, and he explains the reasoning behind it here: The Maze Cube You can buy sticker...

[...] or that it does have meaning, and it is simply false, since there are no colorless green ideas, and therefore there can't be any sleeping, furiously or otherwise. In mathematical logic such a statement would be considered true. Non-existent objects have any property you can name because to pr...

You have X_{t+1} = (aX_t + c) mod 2^k You can simply look at it mod 2^1: X_{t+1} = (aX_t + c) mod 2 The resulting lowest bit of X_{t+1} does not depend on any of the higher bits of X_t, only on the lowest bit. Therefore, this reduced PRNG essentially has an internal state consists only of a single b...

Hmm, watching the videos, I don't like the solutions presented. The originating person's proposal is, with the extraneous stuff removed: 1. Number all the people 1-8. 2. Get cards numbered 1-8, in order. Cycle the deck (move top card to bottom) a random number of times. 3. Give the first ca...

Yeah, with x(t) and y(t) plotted on an x-y plane, maximizing x and y at the same time means having a cusp that "points" toward the top-right. cusp.png Such a cusp is not a general feature of parametric plots, and it's irrelevant (to the general case) that if your graph is just a line segm...

With 7 people you can use two rules. Rule one - If you see four people with the same color, then you must guess that you have the opposite color. Win - 70/128 Lose - 42/128 Rule two - If you see six people with the same color, then you must guess that you have the opposite color Win - 14/128 Lose -...

It is not stated clearly in the question, but I assume that each hat's colour is chosen independently, 50:50 either colour. What you say is true if you make a fixed choice beforehand about who is going make a guess. However, you don't have to do that. For example, consider the smaller version of the...

Maybe at some point the y spelling had dots added because as I wrote before the letter y is not used much normally. In cursive handwriting the ij is essentially identical to y apart from the dots, and it is very hard to resist the urge to automatically add them. That is really interesting. Is this ...

Non-English 26ers include Dutch (Ij directly replacing Y, it seems, a detail to which I would clearly defer to any Dutch forumite who cared to comment) I'm Dutch, so let me wade in here about the Dutch "IJ". It represents a vowel sound, one of the many diphthongs spoken Dutch has. It is n...

See I thought that when you made cards like these it was what he was asking about. I thought these worked, Meets all his conditions. 1376524 1745632 1234567 1472635 1563472 1625743 All your cards have the same symbols. We don't care about their order on each card, so every pair of cards in your set...

Non-English 26ers include Dutch (Ij directly replacing Y, it seems, a detail to which I would clearly defer to any Dutch forumite who cared to comment) I'm Dutch, so let me wade in here about the Dutch "IJ". It represents a vowel sound, one of the many diphthongs spoken Dutch has. It is n...

By the way, having the observers moving instead of stationary does not change the difficulty of this question. Are you dropping the implicit assumption that the objects in the space are stationary? I guess so, because I never really thought of the objects as stationary. *since the line end points r...

Sure. I'm trying to understand the point? Do you think her/his problem is solvable? The OP is not clear: If both points are stationary is it trivial to determine whether or not they can see each other. However, both points are moving. As you said, and I agree, that part is still essentially trivial...

There are two points in a space. The space is filled with objects. If both points are stationary is it trivial to determine whether or not they can see each other. However, both points are moving. Luckily, they are moving in straight lines with a constant speed. How would I go about determining at ...

Read what was written in the picture : "At right you have samples of isosceles triangles connecting three circles" Is there any precision about right triangle or not? no. So triangles could be right or not. Just watch carefully my examples : you have right triangles and not right triangle...

Are you getting that 20 words/sentence average from your personal digital copy? I admit that is an awful lot. On the other hand, by Shane Snow's calculations , Hemingway's books have an overall Flesch-Kincaid reading level of 4, and reading ease of a startling 95. So clearly it matters which metric...

Question: Here in the US decimal numbers are written with a "decimal point " as e.g. 3.14, which is said out loud as "three point one four". I know that in some (many?) other countries decimals are written using a comma as 3,14. In this case how is the number said out loud? Is i...

This what I don't understand - my assumption (perhaps mistaken) is that the Oracle program must have the last move (i.e., it must say that whatever's been fed to it will halt or that what's been fed to it will loop forever). Is that assumption incorrect? That is correct. If you had a perfect Oracle...

I think I have an O(log(N)) solution. Let A initially be {1, 2, 3, ..., N-1}. At all times, we know that at least one of the numbers is in A. Divide A into three roughly equal sets A 1 , A 2 , and A 3 , and ask about A 1 ∪ A 2 , A 1 ∪ A 3 , and A 2 ∪ A 3 . If we get a "yes" response to on...

That is an interesting question. Of course, in the episode the problem was fixed by adding two people who hadn't swapped yet, which adds enough available swaps to always make it solvable. It looks like there's some parity rule that forces complete paths to have an even number of steps, but I'm not s...

But for an object rolling without slipping, some of the gravitational potential energy is transformed into rotational energy. If I do the calculations right, the proportion depends on the ratio of the moment of inertia of the object and the product of its mass and the square of its rolling radius, ...